This paper studies the behavior of sequences in the maximal ideal space of the algebra of bounded analytic functions on an arbitrary domain. The main result states that for any such sequence, either the sequence has an interpolating subsequence or infinitely many elements of the sequence lie in the same Gleason part. G(<p) = {t G M(H°°(Q.)): dn(<p,T) < 1}. A sequence (<pn)™=x c M(H°°(Q)) is called an interpolating sequence if for every bounded sequence of complex numbers (A")JJ1, , there exists

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... / G 77°°(Q) such that <P"(f) = ^n for every « G Z+; here Z+ denotes the set of positive integers.